{"paper":{"title":"New quantum codes from constacyclic codes over finite chain rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Heqian Xu, Ting Yao, Xiaoshan Kai, Yongsheng Tang","submitted_at":"2024-08-28T06:19:42Z","abstract_excerpt":"Let $R$ be the finite chain ring $\\mathbb{F}_{p^{2m}}+{u}\\mathbb{F}_{p^{2m}}$, where $\\mathbb{F}_{p^{2m}}$ is the finite field with $p^{2m}$ elements,\n  $p$ is a prime, $m$ is a non-negative integer and ${u}^{2}=0.$ In this paper, we firstly define a class of Gray maps, which changes the Hermitian self-orthogonal property of linear codes over $\\mathbb{F}_{2^{2m}}+{u}\\mathbb{F}_{2^{2m}}$ into the Hermitian self-orthogonal property of linear codes over $\\mathbb{F}_{2^{2m}}$. Applying the Hermitian construction, a new class of $2^{m}$-ary\n  quantum codes are obtained from Hermitian constacyclic s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.15558","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.15558/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}